Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Friday, March 15, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G11

Speaker: Christoph Lenzen (Massachusetts Institute of Technology)

Early-deciding Consensus is Expensive

In the consensus problem, n nodes seek to agree on one of their input values despite up to t failing nodes. For this task, it is known that synchronous deterministic algorithms cannot guarantee that, in all executions with at most f faults, all correct nodes decide in round f or earlier on the output. This holds even if nodes may merely crash, i.e., in some round send a subset of the scheduled messages and then cease running the algorithm. For Byzantine, i.e., worst-case, behavior of faulty nodes, we prove that it is impossible to guarantee decision in f+2 rounds.

However, the main focus of the talk is the number of messages sent by algorithms achieving these bounds. We show that (f+2)-deciding algorithms that deal with Byzantine faults must send Omega(t2f) messages in some execution with f faults. In the case of crash faults, where (f+1)-decision is possible, matching this bound is even more expensive: Omega(n2f) messages must be sent, regardless of t. In contrast, one can easily achieve (f+1)-decision with O(nt) messages for so-called orderly crash faults, where algorithms specify an order on the messages of each round and crashing nodes successfully send a prefix of the message list according to this order.

The talk will address a general audience; no previous knowledge on consensus is assumed.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login